FIGS. 1A and B show side by side for comparison, diagrams of forces acting on a modern fighter airplane in a steep turn, and forces acting on a modern submarine executing a fast turn while fully submerged.
Referring first to FIG. 1A, as the fighter plane executes a steep turn, its two half wings pull together to offset the centrifugal force that is tending to pull the plane out of the turn.
Referring for contrast to FIG. 1B, a conventional modern submarine has only one half wing, namely its sail (or conning tower), for offsetting the centrifugal force in a turn. As a result, a convention submarine tends to roll in a turn, and tends to snap roll if a high speed turn is attempted.
FIG. 2 shows a computer simulation of the vortex flow field on a modern submarine hull that is yawed towards the viewer approximately 15 degrees. The sail 22 of a modern attack submarine 10 typically measures 400 to 500 square feet in size and, acting like a lifting wing on its side, generates a side force which is nearly half as large as that created by the two hull vortices 12, 12 that start at the bow and roll upon the lee side of the yawing body of revolution. This side force, centered well above the center of gravity of the submerged submarine, is the cause of the snap roll problem which has prevented routine, high-speed turning maneuvers by modern submarines.